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CIRCULAR MOTION
     
1.   An object of mass 450g moves in a circular path of radius 1.5m.
    It completes 2.5 revolutions per second.
    Calculate
  a) the angular velocity
b) the linear speed of the body
  c) the magnitude of the centripetal force needed to maintain this motion
  d) the work done by this force during 10 revolutions.
     
2.   A mass of 15kg is moving in a circular path at the end of a metal rod 4m long.
    The axis of rotation passes through the other end of the rod and the plane of the motion is horizontal.
    The maximum tension that the rod can tolerate is 5104N.
  a) Draw a diagram showing the force(s) acting on the mass.
     Ignore the force of gravity and assume there are no frictional forces.
  b) Indicate clearly on the diagram the direction in which the mass will move if the rod breaks.
  c) Calculate the maximum linear speed with which the mass can move without breaking the rod.
  d) Calculate the maximum rotational frequency corresponding to this maximum speed.
     
3.   Now consider a situation similar to the one described in the previous question but this time we have a rod 8m long with a mass of 15kg on each end.
    The axis of rotation now passes through the middle of the rod.
    What is the maximum rotational frequency in this case, assuming the rod can still take a maximum of 5104N tension.
     
4.   A 200g mass is moving in a circular path on the end of a light metal rod 0.5m long.
    The axis of rotation passes through the other end of the rod and the plane of the motion is vertical.
    The rotational frequency is 1.2s-1.
  a) Calculate the angular velocity.
  b) Draw two diagrams showing the positions of the mass when the tension in the rod is i) maximum and ii) minimum.
    Label the forces acting on the mass and explain briefly why the tension varies.
  c) Calculate the magnitudes of the maximum and minimum tensions.
  d) Calculate the angular velocity at which the minimum tension is zero.
     
5.   A body of mass 2kg is attached to a string 1m long and moves in a horizontal circle of radius 50cm, as shown below.
     
   
     
    This arrangement is often called a "conical pendulum".
  a) Calculate the magnitude of the tension in the string.
  b) Calculate the time period of the motion (the time to complete one revolution).
     
6. a) At what angle should a road surface be banked in order that a vehicle can go round a bend of radius 55m at a speed of 40kmh-1?
  b) Suppose that a vehicle attempts to go round this bend at 100kmh-1.
    If the coefficient of friction between the wheels of the vehicle and the road surface is 0.25, and the mass of the vehicle is 1.5tons (1500kg), will the vehicle skid or not?
    Show your calculations.
     
7.   A body, of mass m, is moving in a circular path of radius r
    The centripetal force acting on it is Fc
    Show that the rotational frequency of the motion is given by
   
 
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